The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  1 X^2+X  1  X  1 X^2+X  1  1  X  1 X^2+X  1 X^2+X  X  1 X^2  1  1  0  0  1 X^2+X  1  0 X^2+X  1  1  1  1 X^2  1  1  1  1  X  1  1  0  X  X X^2  1  1  1  1  1  X X^2+X  0  1  1  1  1 X^2+X X^2  1  1  1  X  0 X^2+X  1
 0  1  0  0  0 X^2 X^2 X^2  1  1  1 X^2+X+1 X+1 X+1 X^2+X+1  X  X X+1  1 X+1  1  X X^2+1 X^2 X^2  0 X^2+X  1  1 X^2+X X^2+X  1 X^2  1  1 X^2+1  1  0 X^2+X  1 X^2 X^2+X  1 X^2 X^2 X^2+X+1 X^2+X X^2+1  X  1  X X^2+X  1 X^2+X  1  1  X X^2+X+1 X^2+1 X+1 X^2  1  1  0  0 X^2+1  X  0  1  1  1 X^2+1  0  1  1  1 X^2
 0  0  1  0 X^2  1 X^2+1  1 X+1  0 X+1 X^2+1 X^2  0  1  X  1  1 X+1 X^2+X X^2+X+1 X+1 X^2+1  X X+1  1  0  0  X X^2+X+1  1 X+1 X^2 X+1  X X^2+X+1 X^2+1 X^2+X X^2 X+1 X^2+1 X^2 X^2+X+1  X  1  X X^2+X+1 X^2+1 X^2+1  0 X^2+X X^2+X  1  1 X^2+X X^2+1  0 X^2  X X+1 X^2+X X^2  X  X X^2+X+1  0  1  1 X^2+X+1 X^2+X  X X+1 X+1 X^2+X X^2+1  X X^2+X
 0  0  0  1 X^2+X+1 X^2+X+1  0 X+1 X^2  1 X^2+1 X^2+X+1 X+1 X^2  0  0 X^2  1 X+1  0 X^2 X^2 X^2+X  1 X+1 X^2+1 X+1 X^2+X+1  X  1 X^2+X X^2+X+1 X^2+1 X^2+X X^2+X+1  0  X  1  1  1  X  0 X^2+1  0  X  X X^2+X X^2+1 X+1 X^2+1 X^2+X X^2+X+1 X^2 X^2+1 X+1 X+1 X^2+X  X  1 X^2+X+1 X^2+X  0 X^2  1  1  X  X X^2+1  X  0  X  0 X^2+X+1 X^2 X^2 X+1 X+1

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+216x^71+306x^72+466x^73+374x^74+346x^75+413x^76+346x^77+309x^78+302x^79+194x^80+170x^81+130x^82+168x^83+109x^84+78x^85+54x^86+50x^87+24x^88+24x^89+4x^90+6x^91+4x^93+1x^94+1x^96

The gray image is a linear code over GF(2) with n=308, k=12 and d=142.
This code was found by Heurico 1.16 in 0.886 seconds.